1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Vector subtraction

  1. Jun 11, 2012 #1
    1. The problem statement, all variables and given/known data

    For the vectors [itex]A^{→}[/itex] and [itex]B^{→}[/itex], calculate the vector difference [itex]A^{→}[/itex] - [itex]B^{→}[/itex]. Magnitude of vector [itex]A^{→}[/itex] is 12 meters, with an angle of 180°. Magnitude of vector [itex]B^{→}[/itex] is 18 meters, with an angle of 37°.

    2. Relevant equations

    [itex]A{y}[/itex] = Asinθ; [itex]B{y}[/itex] = Bsinθ
    [itex]A{x}[/itex] = Acosθ; [itex]B{x}[/itex] =Bcosθ
    Resultant vector = [itex]\sqrt{Rx^{2} + Ry^{2}}[/itex]

    3. The attempt at a solution

    I know not providing a graph might make this problem a bit more difficult. I just really desperately need help on how to calculate vector subtraction because I'm not sure if I'm doing it right.

    I found that the x-component of vector [itex]A^{→}[/itex] is -12 meters and the y-component is 0 meter. The x-component of vector [itex]B^{→}[/itex] is 14.4 meters and the y-component is 10.8 meters. From that, the [itex]R{x}[/itex] would be 2.4 meters and [itex]R{y}[/itex] would be 10.8 meters.

    If I were to just do vector [itex]A^{→}[/itex] + [itex]B^{→}[/itex], I know how to calculate that. I would use the Resultant vector formula [itex]\sqrt{Rx^{2} + Ry^{2}}[/itex], which would give me of R = 11.06. But if I'm doing what this problem is doing, I don't know if that's the right formula to use.

    I understand that [itex]A^{→}[/itex] - [itex]B^{→}[/itex] is the same thing as -[itex]B^{→}[/itex] + [itex]A^{→}[/itex]. I was wondering how the negative part translated into the calculation. For example, do I make vector [itex]B^{→}[/itex]'s x-component negative (to -14.4 meters), and have the [itex]R{x}[/itex] = -26.4 meters and the [itex]R{y}[/itex] = -10.8 meters (because vector [itex]B^{→}[/itex]'s y-component would then be -10.8 mters)? And if all that is correct, would I carry on with the same resultant vector formula [itex]\sqrt{Rx^{2} + Ry^{2}}[/itex], plugging in the numbers to get R = 28.5 meters?

    Thank you so much for helping me!
  2. jcsd
  3. Jun 11, 2012 #2


    User Avatar
    Homework Helper

    The problem asks the vector difference, not only the magnitude of the difference vector. The components of the resultant difference vector are Ax-Bx and Ay-By.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook